Schrieffer-Wolff Transformation on IBM Quantum Computer

Abstract: Schrieffer-Wolff transformation (SWT) has been extensively used in quantum many-body physics to calculate the low energy effective Hamiltonian. It provides a perturbative method to comprehend the renormalization effects of strong correlations in the quantum many-body models. The generator for Schrieffer-Wolff transformation is calculated usually by heuristic methods. Recently, a systematic and elegant method for the calculation of this extremely significant transformation has been reported [1]. Given the huge significance of SWT for many areas including quantum condensed matter physics, quantum optics and quantum cavity electrodynamics, it is imperative to develop quantum algorithm for carrying out SWT on quantum computer. In this paper, we put forward this quantum algorithm and demonstrate it for single impurity Anderson model (SIAM), thereby arriving at Kondo model as effective Hamiltonian. We implement our quantum algorithm in QisKit and carry out SWT for SIAM on IBM Quantum computers. To the best of our knowledge, this work is the first of its kind to obtain Kondo model from Anderson impurity model using a quantum algorithm.